Question

The graph f(x)=x^2 was transformed to create the graph g(x)=−(3x)^2.

Which statement describes this transformation?


a reflection over the x-axis and a horizontal compression

a reflection over the y-axis and a horizontal compression

a reflection over the y-axis and a vertical compression

a reflection over the x-axis and a vertical compression

Answer 1

the first one.

Explanation:

the "-" sign simply turns everything upside-down. what was originally above the x-axis is now below it, and what was below the x-axis is now above it. hence : a reflection over the x-axis.

and 3x compared to x simply makes us race "faster" along the x-axis. we get now at x the functional value we would have gotten at 3x with the original function. so, the function graph appears compressed in the left-right (horizontal) direction compared to the original graph.